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1 GEOPHYSICAL RESEARCH LETTERS, VOL. 37,, doi: /2010gl045386, Rapid Southern Ocean front transitions in an eddy resolving 2 ocean GCM 3 Andrew F. Thompson, 1 Peter H. Haynes, 1 Chris Wilson, 2 and Kelvin J. Richards 3 4 Received 14 September 2010; revised 16 October 2010; accepted 19 October 2010; published XX Month [1] The formation of persistent multiple fronts is an estab- 6 lished feature of the Antarctic Circumpolar Current (ACC). 7 Front strength and location are closely linked to eddy prop- 8 erties and therefore have important implications for the 9 eddy driven closure of the Southern Ocean meridional over- 10 turning circulation. ACC front structure is analyzed here by 11 calculating regional probability density functions (PDFs) of 12 potential vorticity diagnosed in an eddy resolving ocean 13 general circulation model. Rapid spatial transitions in the 14 number of fronts and in the density classes over which they 15 occur are found. Front transitions are associated with the 16 major topographic obstacles Kerguelen Island, Campbell 17 Plateau and Drake Passage; multiple fronts are preferentially 18 found downstream of these features. These findings high- 19 light the significant departure from zonal symmetry of 20 the ACC front structure and emphasize the importance of 21 local dynamics on large scale Southern Ocean properties. 22 Citation: Thompson, A. F., P. H. Haynes, C. Wilson, and K. J. 23 Richards (2010), Rapid Southern Ocean front transitions in an 24 eddy resolving ocean GCM, Geophys. Res. Lett., 37,, 25 doi: /2010gl Introduction 27 [2] Water mass properties in the Antarctic Circumpolar 28 Current (ACC) are observed to be concentrated in multiple 29 fronts [e.g., Sokolov and Rintoul, 2009]. These fronts are 30 often collocated with strong zonal jets, similar to examples 31 in other geophysical contexts [see Baldwin et al., 2007, and 32 references therein], including the Earth s atmospheric jet 33 stream and multiple jets in large planetary atmospheres. In 34 all of these examples, the formation of fronts and jets arises 35 from interaction between eddies and mean flow and implies 36 a strong spatial variation of eddy transports. In the ACC 37 eddy transport plays a major role in the dynamics of the 38 Southern Ocean meridional overturning circulation (MOC), 39 which influences water mass formation, meridional heat 40 transport and carbon dioxide uptake. Variations in eddy 41 transport thus have important implications for the MOC and 42 hence the global climate system. 43 [3] Potential vorticity (PV) is widely accepted as a valu- 44 able dynamical diagnostic in a large class of geophysical 45 flows. In the ocean PV is materially conserved along iso- 46 pycnals in the absence of frictional processes or diapycnal 1 Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK. 2 National Oceanography Centre, Liverpool, UK. 3 School of Ocean and Earth Science and Technology, University of Hawaii at Manoa, Honolulu, Hawaii, USA. Copyright 2010 by the American Geophysical Union /10/2010GL mixing, which are generally weak in the interior of the ACC. 55 PV distributions, as that of any materially conserved scalar, 56 therefore encodes important information about eddy trans- 57 port. In other applications, such as transport of stratospheric 58 chemical species [Sparling, 2000], probability density 59 functions (PDFs) have been used as an effective means of 60 describing spatial variations and identifying important fea- 61 tures. Indeed, Marshall et al. [1993] used PDFs to demon- 62 strate PV homogenization in a simple dynamical model of 63 the ACC and with a coarse resolution hydrographic data set. 64 [4] A feature of the Southern Ocean that distinguishes it 65 from the atmosphere is the fronts strong departure from 66 zonal symmetry. Sokolov and Rintoul [2007, 2009] used 67 satellite altimetry to identify as many as twelve ACC fronts 68 that undergo persistent merger and divergence events and 69 modulations in intensity along the path of the ACC. 70 Shuckburgh et al. [2009] used velocity fields derived from 71 satellite altimetry to advect a passive tracer and calculate an 72 effective diffusivity [Nakamura, 1996] over local patches 73 of the ACC. Effective diffusivity profiles differed between 74 patches providing evidence for mixing variations along the 75 path of the ACC. This paper goes beyond these previous 76 studies by analyzing, using PDFs of PV, the ACC s multiple 77 front structure, as manifested in subsurface PV distributions, 78 and by identifying sharp zonal transitions. By summarizing 79 large amounts of data efficiently, PDFs of PV can provide 80 an excellent tool for detecting both horizontal and vertical 81 transitions in front structure and for indicating key regions 82 that have a dynamical influence on the MOC Data and Methods [5] The temporal and spatial distribution of PV, q = 85 r 1 (f + z) s 2 / z, is calculated using numerical output from 86 the 1/10 degree OfES primitive equation model (Ocean 87 General Circulation Model for the Earth Simulator) 88 [Masumoto et al., 2004] and interpolated onto isopycnal 89 surfaces. Here f is the Coriolis frequency, z = u y v x is 90 relative vorticity, s 2 is potential density referenced to 2000 m 91 (units of kg m 3 understood) and r is in situ density. OfES 92 includes 54 vertical levels with a realistic bathymetry. The 93 model has high spatial and temporal resolution and solves a 94 dynamically consistent set of equations relevant to the 95 Southern Ocean. Our approach is to regard this as a useful 96 surrogate for the real Southern Ocean. In fact, the PV dis- 97 tributions extracted from OfES are broadly similar to those 98 generated from the Southern Ocean State Estimate (SOSE) 99 model [Mazloff et al., 2010], which has a coarser resolution 100 (1/6 degree), but includes data assimilation. 101 [6] Construction of a reliable PDF requires a sufficiently 102 large number of data points. Our approach is to use a single 103 snapshot of the PV field, but calculate PDFs from a sam of5 84

2 Figure 1. (a) Snapshot of potential vorticity PV ( [ms] 1 ) on the s 2 = potential density surface in the Southern Ocean of the eddy resolving OfES model. Land and isopycnal depths shallower than 100 m are colored white. Contours indicate isopycnal depth, with the 500, 1000 and 1500 m isolines plotted. (b) Isopycnal depth (m) over the region 180 W to 140 W and (c) an expanded view of PV in this region. (d) Probability density function of PV values in Figure 1c, normalized by the mean PV; the non linear colorscale in Figures 1a and 1c is mapped onto the abscissa. (e) Snapshot of PV on the s 2 = potential density surface. Contours indicate the 1000, 2000 and 3000 m isolines of isopycnal depth. Markers above Figure 1a indicate key topographical features: CA, Cape Agulhas; CI, Crozet Island; KI, Kerguelen Island; Tas, Tasmania; CP, Campbell Plateau; UFZ, Udintsev Fracture Zone; DP, Drake Passage; SGI, South Georgia Island. 105 pling region with finite zonal width. Choosing this width as was found to be large enough to give robust PDFs and 107 small enough to show significant zonal variation. The 108 sampling regions span 65 S to 40 S and were further 109 required to contain at least 2000 grid points. Temporal 110 variability is discussed below Results 112 [7] Figure 1a shows a typical snapshot of PV on the s 2 = potential density surface with land masses and fluid at 114 a depth less than 100 m colored white. The PV distribution 115 is dominated by a large scale gradient, but mesoscale eddies 116 give rise to regions of sharper and weaker PV gradients. A 117 region of particularly well defined fronts is found down- 118 stream of the Campbell Plateau (CP) between 180 W and W (Figures 1b and 1c). Figure 1d displays a PDF of PV 120 over the region in Figure 1c, normalized by the mean PV in 121 this region; the non linear color scale in Figures 1a and 1c is 122 mapped to the abscissa. PV is found in four distinct pools 123 (PDF maxima) separated by three fronts (PDF minima). At 124 greater depths the influence of topography becomes stron- ger, as shown by a snapshot of PV along the s 2 = potential density surface (Figure 1e). Here topographic obstacles may shield and isolate regions of the ACC, which induce significant regional variability in the meridional PV gradient. Indeed, reversals in the sign of the large scale PV gradient occur at 30 E, 80 E, 120 W, and 60 W. As linear instability properties of the ACC depend on the vertical structure of meridional PV gradient [Smith and Marshall, 2009], variations in this gradient will have important implications for regional differences in eddy characteristics along the path of the ACC. [8] In Figure 1d, a line plot PDF of PV is calculated over a sampling region on an isopycnal surface. By slowly changing the mean longitude/isopycnal of the window (now using a 10 zonal extent), horizontal/vertical variations in the front structure can be identified. Figure 2 shows the accumulation of PDF line plots on the s 2 = (Figure 2a), s 2 = (Figure 2b) and s 2 = (Figure 2c) density surfaces as the sampling region is shifted along the path of the ACC. Warm colors indicate high probability of the corresponding PV value on the ordinate; the thin black curves mark local maxima of the individual PDFs (cf of5

3 Figure 2. Probability density function (PDF) of potential vorticity (PV) as a function of longitude on the (a) s 2 = 36.36, (b) s 2 = and (c) s 2 = potential density surfaces. The PDFs are normalized by the mean PV in each window (see text for full discussion). The thin black lines mark local maxima of the individual PDFs. The full vertical extent of the PDFs along the white dashed lines is (d) 140 E and (e) 160 W. The black lines correspond to the isopycnals in Figures 2a 2c and the black dots mark local maxima of the individual PDFs. Markers showing the position of key topographical features are defined in the caption of Figure Figure 3). Figures 2d and 2e show the accumulation of 148 PDF line plots on different isopycnals at the longitudes 149 indicated by the dashed lines in Figures 2a 2c. Again, 150 warm colors indicate PDF maxima, corresponding to regions 151 of homogenized PV. Major topographical features are 152 marked along the top of Figure 2a for reference. [9] PV front structure varies significantly both along the path of the ACC and in the vertical. In particular, Figure 2a shows distinct partitioning of PV along the s 2 = isopycnal. Immediately downstream of Kerguelen Island (KI, 70 E) PV has a largely uniform value around m 1 s 1, which may be related to mixing occurring Figure 3. Number of distinct homogenized pools of potential vorticity (PV) as a function of longitude and potential density surface. Distinct PV pools are determined by the number of local maxima in a probability density function (PDF) of PV on a given isopycnal surface spanning 10 longitude and 25 latitude. Large values are indicative of multiple fronts. Markers showing the position of key topographical features are defined in the caption of Figure 1. 3of5

4 Figure 4. Two year evolutions of PV PDFs over the regions (a) 180 W to 140 W (Figure 1c) and (b) 120 W to 80 W on the s 2 = isopycnal. 159 over and around this large topographic obstacle. Further 160 downstream in the Indian Sector, three to four distinct fronts 161 occur that are associated with the northern flank of the ACC 162 and a zonally oriented ridge south of Australia. On this 163 shallow isopycnal, PV is largely uniform over the Pacific 164 sector of the ACC, consistent with PV homogenization in 165 the South Pacific gyre circulation [Marshall et al., 1993]. A 166 rapid change in the outcropping latitude of this isopycnal 167 through Drake Passage (DP) contributes to the step like 168 transition in PV near 60 W. Multiple fronts found south of 169 Cape Agulhas (CA, 20 E) reflect contributions from the 170 core of the ACC as well as from the Agulhas retroflection. 171 Along the s 2 = isopycnal (Figure 2b), multiple dis- 172 tinct PV pools are found in the Pacific sector, particularly 173 above the abyssal plains downstream of the Udintsev 174 Fracture Zone (UFZ, 145 W). On this particular isopycnal 175 the signature of multiple fronts is much weaker downstream 176 of KI. PV structure along s 2 = (Figure 2c) is strongly 177 constrained by topography as suggested by Figure 1e. Iso- 178 lated patches of PV can lead to abrupt changes in the 179 meridional PV distribution, e.g., the low PV values near E and the large PV values near 90 W. 181 [10] Vertical transitions in PV structure also exhibit 182 regional differences. In the Indian sector (Figure 2d), distinct 183 PV pools are found within the density class 36.1 < s 2 < 36.5, 184 associated with the northern boundary of the ACC. These 185 collapse to nearly uniform PV along the s 2 = 36.6 isopycnal 186 surface, which is reflected in a weak PV gradient on this 187 isopycnal. Distinct pools of homogenized PV are then found 188 at deeper isopycnals. In the Pacific sector (Figure 2e), PV is 189 largely homogeneous on isopycnals where s 2 < 36.5, as 190 discussed above. On deeper isopycnals, three to four distinct 191 PV pools are found as indicated by the black dots. 192 [11] The particular isopycnals and longitudes displayed in 193 Figure 2 are representative of the different horizontal and 194 vertical variability apparent in the PV structure. However, 195 these individual running PDFs do not provide a compre- 196 hensive view of PV front characteristics. In Figure 3 the 197 information from the PDFs is collapsed into a single plot by 198 calculating the number of independent maxima from each of 199 the windowed PV PDFs, e.g., the black curves and black 200 dots in Figure 2. A relatively crude method is employed to 201 count the maxima: to qualify, a local maxima must be a 202 threshold value greater than both neighboring local minima. 203 Figure 3 uses a threshold value of , although the 204 qualitative pattern that emerges is largely insensitive to the 205 threshold value. Thus Figure 3 shows the number of maxima, or distinct pools of PV, as a function of longitude and isopycnal surface (PDFs are still calculated using a 10 zonal extent). [12] Figure 3 shows clear transitions in front structure at the major topographical obstructions KI, CP and DP. Interpretation of this plot requires care because, as seen in Figure 1, isopycnal surfaces may span a large depth range across the ACC, and different density classes may be found in the core of the ACC in different locations. PV on shallow isopycnals on the northern flank of the ACC appears to be homogenized throughout much of the Southern Ocean with the exception of the region downstream of KI. The isopycnal surface s 2 = appears here as a surface of uniformly small number of peaks, and is the lower boundary of the shallow homogenized PV region in the Pacific sector. In the Indian sector of the ACC ( 120 E), multiple fronts are found in two different density classes, reflecting front formation on both flanks of the ACC, whereas in the Pacific sector ( 120 W) there is only a single density class exhibiting multiple fronts. There is some evidence of multiple fronts in two density classes in the Atlantic sector, however the transition is found at shallower isopycnals than in the Indian sector. The major topographical features are also associated with a reduction in the number of fronts near or just downstream of the obstruction. [13] Temporal variability of the PDFs of PV is, to a degree, spatially dependent. Front structure associated with topographically constrained jets is largely stationary, as in Figure 4a, which shows the time evolution of the PV PDF corresponding to the region in Figure 1c. On the same isopycnal (s 2 = 36.74) in the eastern Pacific sector, where topography is relatively flat, the amplitude and location of the PDF maxima are more variable (Figure 4b), which may arise from either forcing variability or internal variability. Still, the number of distinct PV fronts remains largely constant over this period. This, then, supports the assertion that snapshots, like Figure 3, provide a useful representation of the longer term front structure, certainly on time scales of many months. 4. Discussion [14] Complicated eddy processes in the ACC influence global climate through their effect on the MOC and are manifest in a complex structure of jets and fronts. Here we have resolved the spatial (and to an extent temporal) variability of the ACC s front structure by employing a novel of5

5 251 diagnostic, calculating PDFs of PV on isopycnals, applied to 252 a high resolution ocean GCM. The results show that PV 253 fronts form in specific regions of the ACC and on specific 254 density classes. Rapid alongstream transitions between these 255 regions are detected for the first time. The significant ver- 256 tical and alongstream variability of the front structure is 257 consistent with the spatially dependent mixing described by 258 Shuckburgh et al. [2009] and Abernathy et al. [2010], but 259 here identification of sharp changes in front structure point 260 to regions that are likely to exert dynamical control over the 261 MOC and merit further study. 262 [15] PDFs are an efficient means of analyzing a large 263 amount of complicated data. Because of this, it can be dif- 264 ficult to determine with certainty the physical processes 265 responsible for the observed transitions in front structure. 266 Still, the correlation between front transitions and topo- 267 graphical features is remarkable. Topography acts to both 268 steer mean flows and modify PV gradients, and these 269 changes may feed back on eddy generation through baro- 270 tropic and baroclinic instabilities [Thompson, 2010], leading 271 to enhanced mixing. Figure 3 shows evidence of these local 272 dynamical processes as immediately downstream of the 273 major topographical constrictions KI, CP and DP there is a 274 full depth reduction in the number of homogenized pools of 275 PV. We note that topographical features also tend to be sites 276 of internal wave generation that can enhance diapycnal 277 mixing and modify interior PV. It is not well known at 278 present how vertical mixing impacts front structure. Finally, 279 topography may also alter PV distributions through mod- 280 ifications in stratification related to rapid changes in iso- 281 pycnals that outcrop or in outcrop locations; this is 282 especially evident across Drake Passage (Figures 2 and 3). 283 Besides being a key sink of momentum input by surface 284 winds, these results indicate that topography also (i) acts as a 285 catalyst for local re organization of water mass structure and 286 (ii) isolates regions of the deep ACC, which affects large 287 scale PV gradients. 288 [16] This study begins to link the work of Shuckburgh 289 et al. [2009] and Abernathy et al. [2010] with Sokolov 290 and Rintoul [2007, 2009]. Multiple jets are found through- 291 out the ACC, but the effectiveness of these jets acting as 292 barriers to transport (i.e., to separate distinct water masses) 293 likely varies along the path of the ACC. Specifically, this 294 study highlights the need to further study the dynamical 295 relationship between fronts and velocity jets in the ACC, 296 including the link between surface fronts and interior PV 297 distributions. Indeed, although Sokolov and Rintoul [2009] 298 identify many circumpolar fronts from altimetry data, 299 Shuckburgh et al. [2009] discover a much smaller number of 300 low mixing regions in certain parts of the ACC using the 301 same data set. This study also indicates that changes in 302 transport properties may occur rapidly and may depend on 303 local dynamics, such as constraints on the flow past topography. This suggests that local dynamics impact global 304 properties of the Southern Ocean and its MOC, and care must 305 be taken in the interpretation of regional observations or of 306 zonally averaged theories of Southern Ocean circulation. 307 [17] The most striking result of this study is the strong 308 zonal variation and the dominant control of topography over 309 the ACC s multiple front structure. This behavior motivates 310 a possible model of the ACC that is comprised of zonally 311 uniform regions separated by sharp transitions. The physical 312 processes that govern the rapid re organization of the front 313 structure at these topographical transition zones is the focus 314 of on going research. 315 [18] Acknowledgments. The authors gratefully acknowledge the pro- 316 vision of OfES output by Hideharu Sasaki and James Potemra. We also 317 thank Matt Mazloff for supplying SOSE output. AFT was supported by 318 NERC, NE/E013171/1. CW was supported by NERC through Oceans and NE/l001794/ References 321 Abernathy, R., J. Marshall, M. Mazloff, and E. Shuckburgh (2010), 322 Enhanced isopycnal mixing at steering levels in the Southern Ocean, 323 J. Phys. Oceanogr., 40, Baldwin, M. P., P. B. Rhines, H. P. Huang, and M. E. McIntyre (2007), 325 The jet stream conundrum, Science, 315, Marshall, J., D. Olbers, H. Ross, and D. Wolf Gladrow (1993), Potential 327 vorticity constraints on the dynamics and hydrography of the Southern 328 Ocean, J. Phys. Oceanogr., 23, Masumoto, Y., et al. (2004), A fifty year eddy resolving simulation of the 330 World Ocean Preliminary outcomes of OFES (OGCM for the Earth 331 Simulator), J. Earth Simulat., 1, Mazloff, M. R., P. Heimbach, and C. Wunsch (2010), An eddy permitting 333 Southern Ocean State Estimate, J. Phys. Oceanogr., 40, Nakamura, N. (1996), Two dimensional mixing, edge formation, and per- 335 meability diagnosed in area coordinates, J. Atmos. Sci., 53, Shuckburgh, E., H. Jones, J. Marshall, and C. Hill (2009), Understanding 337 the regional variability of eddy difusivity in the Pacific sector of the 338 Southern Ocean, J. Phys. Oceanogr., 39, Smith, K. S., and J. Marshall (2009), Evidence for enhanced eddy mixing at 340 middepth in the Southern Ocean, J. Phys. Oceanogr., 39, Sokolov, S., and S. R. Rintoul (2007), Multiple jets of the Antarctic 342 Circumpolar Current south of Australia, J. Phys. Oceanogr., 37, Sokolov, S., and S. R. Rintoul (2009), Circumpolar structure and distribu- 345 tion of the Antarctic Circumpolar Current fronts: 1. Mean circumpolar 346 paths, J. Geophys. Res., 114, C11018, doi: /2008jc Sparling, L. C. (2000) Statistical perspectives on stratospheric transport, 348 Rev. Geophys., 38, Thompson, A. F. (2010), Jet formation and evolution in baroclinic turbu- 350 lence with simple topography, J. Phys. Oceanogr., 40, P. H. Haynes and A. F. Thompson, Department of Applied Mathematics 352 and Theoretical Physics, Centre for Mathematical Sciences, University of 353 Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK. (a.f. 354 thompson@damtp.cam.ac.uk) 355 K. J. Richards, School of Ocean and Earth Science and Technology, 356 University of Hawaii at Manoa, 1680 East West Rd., Honolulu, HI , USA. 358 C. Wilson, National Oceanography Centre, 6 Brownlow St., Liverpool 359 L3 5DA, UK of5